You are planning to invest into two assets. One asset is the ETF fund that tracks returns on the S&P 500 index. The expected return on the index is 10% and the standard deviation of returns on the index is 17%. The other asset is the risk-free Treasury bill with the expected return of 2% per year.

1. You wish to construct a portfolio of these two assets that pays 15% expected return. What are the weights of the two assets in such a portfolio?
2. What do these weights mean? What are your positions: long or short?
3. You have $10,000 to invest. How much money do you invest in each of these two assets to achieve your goal?
4. What is the standard deviation of your portfolio?